How to add more edges in an object
It's not that hard,  but not particularly obvious either.


Switch to edge select mode using the button at the bottom of the 3D view.
Select the edges you want to add vertices to.
Hit W > Subdivide. (Not Subdivide Smooth! Unless you want your new edge to be rounded, which doesn't sound like the case here.)
(Optional) Switch back to vertex mode.


That's all there is to it!